Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits: $$\begin{array}{rl}1634& =1^4+6^4+3^4+4^4\\ 8208& =8^4+2^4+0^4+8^4\\ 9474& =9^4+4^4+7^4+4^4\end{array}$$

As $1=1^4$ is not a sum it is not included.

The sum of these numbers is $1634+8208+9474=19316$.

Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.